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In yet another attempt to reach Rio de Janeiro, the Eleventh Doctor, Amy and Rory end up in the strangest of places. The planet they're on appears to be very civilised; however, they soon find out that it's a place where there is no justice keeping the peace, but crime lords ruling over all.

Cornucopia, 2012. A monkey-like humanoid breaks into a mansion stuffed to the ceiling with precious artefacts. He steals a red jewel called the Star of Solitude and replaces it with a fake. As he makes his escape, the TARDIS materialises, and the Doctor emerges, wearing a ridiculous hat, thinking himself to be in Rio. Amy and Rory soon follow, unimpressed. The Doctor looks at the collection in wonder, saying that there is stuff from all over the galaxy. He can't think of how they're all connected. Rory points out that if they're valuable they'll be well guarded, and the alarm sounds. Alien security guards storm the room and chase the three, who are split up in the chaos. Amy is cornered by two guards, and is rescued by the monkey man, who escapes with her using a hover-board. The Doctor and Rory are captured, and a green lizard-like humanoid enters, introducing herself as Granny Solasta and informing them that it is her collection. The Doctor tells her that they are police, showing her the TARDIS, and she orders her men to kill them.

The monkey man introduces himself as Horatio Lynk and the planet as Cornucopia. He complains at Amy for ruining his reputation as the best thief on Cornucopia, and she thanks him for saving her life.

Granny tells the Doctor and Rory that police are illegal in Cornucopia, and orders one of her men to phone the Assassins Alliance for formal murder. A blue insect-like humanoid, Miss Ghost, enters and tells Granny to cancel the call, showing her footage of the TARDIS materialising. Granny agrees that maybe she has been a little hasty.

Amy and Horatio are stopped by the Hijackers Guild, who prepare to board them. They fly away and the hijackers give chase, firing null-charges at them and eventually hitting Lynk, knocking him unconscious. They then destroy the board, and Amy and Horatio fall towards the ground hundreds of feet below.

Amy uses one of Horatio's wrist-gadgets to deploy a grappling hook, and swings them both to safety. The hijackers arrive, but realise that since they are no longer on a vehicle hijacking is impossible. As they fly away, Amy wakes Lynk up with a bucket of water.

The Doctor shows Solasta inside the TARDIS, and he remembers what all the artefacts in the collection have in common: They were all stolen. Granny tells him she is the head of ThiefCorp, behind all the biggest jobs of the last century. The Doctor works out that Lynk stole the Star of Solitude and replaced it with a fake. He wonders why the thief took the only thing in the room that he didn't recognise.

Lynk takes Amy to a street with many different species making their way around. He explains that they are all natives, and Cornucopia used to be a space port. However, traffic dried up and the poorest had no way off the planet. A rad-storm had been blowing in the ionosphere for about a century, blocking every radio wave, resulting in the spacecraft having to land by sight. A woman, Mrs Mintus, stops them and thanks Lynk for helping her child get food and vaccinations. They move on, and Amy asks for his help in finding her friends. They are stopped by members of the Kidnappers Federation. Lynk tries to fight them off, but is hit around the head and knocked down. Amy picks up a gun that one of the kidnappers dropped and accidentally shoots, catching them all in an electrified net. Horatio tells her it is a somna-net, and that they'll be out cold for hours. He shows her the Ziggurat of Cornucopia, one of the eight wonders of the universe, which appeared above the city a century ago. Nobody has been able to breach it or unlock its doors.

Granny tells the Doctor to make himself at home, and Miss Ghost introduces her guests, the Crime Lords: Professor K'rokk of the Assassins Alliance, Deacon Kell of the Blackmailers Collusion, Lady Panibri of the Hijackers Guild, and Brother Traybe of the Kidnappers Federation. As the Doctor mingles with the guests, Rory spots a tiny creature named Godo tied to a stick on a platter. It begs him to help, but K'rokk picks it up and eats it by consuming it in flames. Rory asks the Doctor why they're dining with the crime lords instead of searching for his missing wife, and the Doctor tells him that these are spectacularly ruthless individuals who will kill them in a heartbeat if he demonstrates the slightest resistance to their authority, and tells him to keep smiling. Granny finally announces her intention: The Doctor is going to take them on board the Bank of Heaven (the Ziggurat) with the TARDIS, and save Rory's life.

At Lynk's house, Horatio produces a cosmic radiation battery, and uses it to test the Star of Solitude; ever since he was one of Granny's students, he's known that the Star is special. As he activates the device, Amy is knocked back by a sudden blast of energy.

The Doctor takes the Crime Lords on board the Ziggurat, which is full of treasures. While they're distracted, Rory suggests that they get away, but the Doctor is distracted himself by the Sphere of Antallos, which he had thought to be lost forever. Rory tells him to forget it, but the Doctor punches him, declaring that the sphere is his.

In retaliation, Rory slaps the Doctor, breaking the Ziggurat's hold on his mind. The Doctor throws the sphere away and explains that the place is filled with emotional energy, as if the air is saturated in greed.

Horatio's test has worked; as he thought, the Star is a teleport key. Amy agrees to go to the Ziggurat with him, but only if he helps her find her friends first. They teleport on board, and Granny's men immediately attack Lynk, who escapes with the star. The Doctor tells Granny she has to leave as the Bank of Heaven is clearly a trap, but she refuses, instead leaving them with the guards. The Doctor reverses the guard's friction-ampers and gives chase.

Horatio enters the neural network command cockpit, and is about to insert the Star, realising it is the ignition key, but is stopped by the Doctor, who tackles him to the ground. They are interrupted by the crime lords, but the Doctor tells them that only one of them can claim the Bank of Heaven, causing them to turn on each other. Traybe kills Panibri, only to be killed by K'rokk. Miss Ghost protests, trying to persuade them to stop, but gives up. Granny kills Kell, leaving only her and K'rokk. Before he can consume her with his flames she blocks her mouth with industrial sealant. With no way to release the energy, K'rokk's internal furnace builds up charge until he explodes. She holds Amy at gunpoint and demands that Horatio gives her the star. He hands it over, but the Star doesn't work. The Doctor reveals that he switched it for the fake one, and destroys the real Star with his sonic screwdriver. In doing so he accidentally starts a self-destruct program, but Granny refuses to leave. Forced to leave her behind, the Doctor, Amy, Rory, Horatio, and Miss Ghost all escape in the TARDIS. The Doctor drags the Ziggurat away from the city, and the citizens marvel at the sight, with Mrs Mintus calling it "hope".

Later, Amy, Rory, and Horatio talk about the radiation storm clearing up. Horatio remarks that Cornucopia could become a real spaceport again. He asks Amy to stay behind, but she tells him she's married. He kisses her anyway, to Rory's distress.

The Doctor explains to Miss Ghost that the ship's pilot died and it came to Cornucopia and ejected its key, knowing an exceptional individual would eventually decipher it. However, Lynk didn't have the greed the ship needed. Miss Ghost scoffs at the idea of a ship being powered by greed, but the Doctor tells her greed powers whole empires. Emotions can be a power source, a very dangerous one. She thanks him for the explanation and shakes his hand, and he asks her to explain something to him: "Who are you?" She looks like a Toliakk, but she was drinking wine with the Crime Lords, which would have fried a real Toliakk's liver in seconds, and everyone was calling his ship a policing box, but somehow she knew it was a TARDIS. Miss Ghost draws a gun and turns off her disguise, revealing herself to be a woman in full armour. She congratulates him for still being the smartest man in the room. The Doctor asks her if they've met before, and she tells him that they have history. The Doctor asks her who she is, but instead of answering she poses a familiar question: What is buried in man? She opens up a portal and leaves, telling him that she'll see him again.